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Law enforcers found a bullet-hit man on the spot who was later declared dead by health officials, reports BBC.
Images from the scene showed medics trying to save a person who appeared to be a white man.
The shooting came amid fights between the Trump supporters and BLM protesters in the city centre.
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Tension rose after a convoy of some 600 vehicles flying flags and carrying an estimated 1,000 Trump backers gathered at a mall in Clackamas county on the outskirts before entering Portland's downtown.
Video showed some people firing what local media described as pepper spray and pellets at BLM groups who had tried to prevent them entering the city by blocking streets.
Portland police said they heard sounds of gunfire from the area of Southeast 3rd Avenue and Southwest Alder Street.
They responded and located a victim with a gunshot wound to the chest. Later, health officials determined that the victim was deceased, they added.
The man was wearing a hat linked to far-right group Patriot Prayer.
However, no disclosure was made whether the shooting was directly related to the clashes in a downtown area.
Portland's streets have witnessed frequent protests in recent weeks. The city has become a focus for demonstrations against police brutality and racism since the police killing of African-American George Floyd in Minneapolis on May 25.